I'm not sure what you call 'extreme cold weather', but I can personally attest that Break Free flows and works at 19 below zero F, just as it does at 70 above F.
I would be wary of grease at low temp ranges like the above, unless it was applied in a very thin film.
I know GOB likes his 3 in 1 oil, but we have to remember, where he lives, ice only comes from the freezer.
